1. Field of the Invention
The present invention relates to recovering the 3-D motion of a thick-walled ellipsoid given 2-D projected movement in the ellipsoid. The third component of motion is inferred via the material constraint of incompressibility. Due to the inherent instability associated with imposing material constraints, the thick-walled ellipsoid is realized with a unique geodesic-based tessellation.
2. Description of the Prior Art
Park, Metaxas and Young developed a thick ellipsoidal model for recovering 3-D cardiac motion from tagged-MR data in "Deformable Models With Parameter Functions: Application To Heart Wall Modeling", Proceedings of the IEEE CVPR, Seattle, Wash., pages 437-442, 1994. Their model formulation differs from the model formulation of the present invention in that their model assumes a dense motion information acquisition and therefore makes no use of "regularizing" constraints such as incompressibility and does not employ a geodesic tessellation.
O'Donnell, Gupta, and Boult presented a thick superelliptic model, the HVV in "The Hybrid Volumetric Ventriculoid: A Model For MR-SPAMM 3-D Analysis", Proceedings of Computers in Cardiology, IEEE, 1995. Their model fitting was influenced via an inter-nodal stretching penalty as opposed to current incompressibility constraint of the present invention. And was tessellated in a simplistic manner.
Finally, T. Denny and J. Prince in "3D Displacement Field Reconstruction From Planar Tagged Cardiac MR Images", Proceedings of the IEEE Workshop on Biomedical Image Analysis, pages 51-60, 1994, employed a multidimensional stochastic model for measuring cardiac motion from tagged-MR images. They used the Fisher estimation framework to approximate the movement of the Left Ventricle (LV) from sparse displacement measurements with incompressibility constraints.